It’s t-22 hours until my econometrics final, I have been studying my ass off, I’m tired, I have no idea what this video is even talking about, I’m hungry and a little scared.

@SheafificationOfG

29 күн бұрын

Did you pass? (Did the universal approx thm help?)

@davidebic

21 күн бұрын

​@@SheafificationOfGusing this theorem he could create a neural network that approximates test answers to an arbitrarily good degree, thus getting an A-.

Came for the universal approximation theorem, stayed for the humor (after the first pump up I didn't understand a word). Great video!

super underrated channel

as someone who is really interested in pure maths, i think that youtube should really have more videos like these, keep it up!

@SheafificationOfG

Ай бұрын

Happy to do my part 🫡

5:07 phew, this channel is gold. Basic enough that I understand whats going on as an applied ML engineer, and smart enough that I feel like I would learn something. Subscribed.

I have no idea what I just watched

Did not expect to see a Jim's Big Ego reference here

To 6:20. The secant line approximation converges at least pointwise. But for the theorem we want to construct uniform/sup-norm convergence, and I don't see why that holds for the secant approximation.

@SheafificationOfG

19 күн бұрын

Good catch! The secret sauce here is that we're using a smooth activation function, and we're only approximating the function over a closed interval. For a smooth function f(x), the absolute difference between df/dx at x and a secant line approximation (of width h) is bounded by M*h/2, where M is a bound on the absolute value of the second derivative of f(x) between x and x+h [this falls out of the Lagrange form of the error in Taylor's Theorem]. If x is restricted to a closed interval, we can choose the absolute bound M of the second derivative to be independent of x (and h, if h is bounded), and this gives us a uniform bound on convergence of the secant lines.

I don't think I'm part of the target group for this video ( i have no idea what the fuck you are talking about) but it was still entertaining and allowed me to feel smart whenever I was able to make sense of anything ( I know what f(x) means) so have a like and a comment, and good luck with your future math endeavors!!

@SheafificationOfG

Ай бұрын

Haha thanks, I really appreciate the support! The fact that you watched it makes you part of the target group. Exposure therapy is a pretty powerful secret ingredient in math.

@6:22 missed opportunity for the canonical recall from gradeschool joke

@SheafificationOfG

20 күн бұрын

😔

your linguistic articulation is extremely specific and 🤌🤌🤌

This is by far the math channel with the best jokes. Sadly, I don't know any Chinese, so I couldn't figure out who 丩的層化 is. Best any translator would give me was "Stratification of ???"...

@SheafificationOfG

Ай бұрын

Haha, thanks! 層化 can mean "sheafification" and ㄐ is zhuyin for the sound "ji"

Great content

I suppose I can show the last equality of 9:04 using induction on monomial operators?

@SheafificationOfG

28 күн бұрын

Yep! Linearity of differentiation allows you to assume q is just a k-th order mixed partial derivative, and then you can proceed by induction on k.

Any videos coming about Kolmogorov Arnold networks?

@SheafificationOfG

Ай бұрын

I didn't know about those prior to reading your comment, but they look really interesting! Might be able to put something together in the future; stay tuned.

Can you share the pdf of the notes you show in the video?

@SheafificationOfG

26 күн бұрын

If you're talking about the source of the proof I presented, the paper is in the description: M. Leshno, V.Y. Lin, A. Pinkus, S. Schocken, 1993. Multilayer feedforward networks with a non-polynomial activation function can approximate any function. Neural Networks, 6(6):861--867. If you're talking about the rest, I actually just generated LaTeX images containing specifically what I presented; they didn't come from a complete document. I might *write* such documents down the road for my videos, but that's heavily dependent on disposable time I have, and general demand.

@korigamik

26 күн бұрын

@@SheafificationOfG then demand there is. I love well written explanations to read not see

@SheafificationOfG

26 күн бұрын

@@korigamik I'll keep debating writing up supplementary material for my videos (though I don't want to make promises). In the meantime, though, I highly recommend reading the reference I cited: it's quite well-written (and, of course, the argument is more complete).

banger vid

@SheafificationOfG

22 күн бұрын

thanks fam

Okay but has the manga good application? Does it train faster or something?😊 (Please help me I like mathing but world is corrupting me with its engineering)

@SheafificationOfG

Ай бұрын

The manga is an enjoyable read (though it's an old paper), but it doesn't say anything about how well neural networks train; it's only concerned with the capacity of shallow neural networks in approximating continuous functions (that we already "know" and aren't trying to "learn"). In particular, it says nothing about training a neural network with tune-able parameters (and fixed size). (I feel your pain, though; that's what brought me to make a channel!)

@kuzuma4523

Ай бұрын

@@SheafificationOfG Fair enough. I'll still give it a read. Also, thanks for the content; it felt like fresh air watching high level maths with comedy; I shall therefore use the successor function on your sub count.